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Nash's doctoral thesis
Non-Cooperative Games, 1951
Details
Nash's doctoral thesis
Non-Cooperative Games, 1951
NASH, JR. John Forbes (1928-2015). "Non-Cooperative Games." Offprint from: Annals of Mathematics, pp. 286-295, Vol 54, No 2, September 1951.
First edition, offprint issue of Nash's doctoral thesis, formulating the theory of non-cooperative games and describing the Nash equilibrium, for which he was awarded the 1994 Nobel Prize in Economic Sciences. In his biographical essay for the Nobel Prize, Nash humbly noted, "As a graduate student I studied mathematics fairly broadly and I was fortunate enough, besides developing the idea which led to 'Non-Cooperative Games,' also to make a nice discovery relating to manifolds and real algebraic varieties. So I was prepared actually for the possibility that the game theory work would not be regarded as acceptable as a thesis in the mathematics department and then that I could realize the objective of a Ph.D. thesis with the other results." It was not only a Ph.D., but also a Nobel Prize. Non-Cooperative Games put forth the concept now widely known as the Nash equilibrium. It provided a framework for analyzing strategic interaction of all kinds, and its reach would be felt from economics to social and biological sciences and beyond.
Octavo (258 x 173mm). Original orange stapled wrappers (some light soiling to covers, a little rusting to staples). Provenance: John Forbes Nash, Jr.
Non-Cooperative Games, 1951
NASH, JR. John Forbes (1928-2015). "Non-Cooperative Games." Offprint from: Annals of Mathematics, pp. 286-295, Vol 54, No 2, September 1951.
First edition, offprint issue of Nash's doctoral thesis, formulating the theory of non-cooperative games and describing the Nash equilibrium, for which he was awarded the 1994 Nobel Prize in Economic Sciences. In his biographical essay for the Nobel Prize, Nash humbly noted, "As a graduate student I studied mathematics fairly broadly and I was fortunate enough, besides developing the idea which led to 'Non-Cooperative Games,' also to make a nice discovery relating to manifolds and real algebraic varieties. So I was prepared actually for the possibility that the game theory work would not be regarded as acceptable as a thesis in the mathematics department and then that I could realize the objective of a Ph.D. thesis with the other results." It was not only a Ph.D., but also a Nobel Prize. Non-Cooperative Games put forth the concept now widely known as the Nash equilibrium. It provided a framework for analyzing strategic interaction of all kinds, and its reach would be felt from economics to social and biological sciences and beyond.
Octavo (258 x 173mm). Original orange stapled wrappers (some light soiling to covers, a little rusting to staples). Provenance: John Forbes Nash, Jr.
Further details
A NOBEL PRIZE THAT NEARLY WASN'T
At one point in the film A Beautiful Mind, when it looked as if things were all over for John Nash, his wife Alicia takes his hand and places it over her heart and says, “I have to believe that something extraordinary is possible.”
Again and again in a life that encompassed genius, madness and reawakening, the extraordinary was possible.
At Princeton in the late 1940s, the 20-year old West Virginian was conspicuous for his movie star looks and Olympian manner. He was six feet, one inch tall, heavily muscled. He wore his fingernails unusually long. His conversation had a stilted, ornamental quality. He avoided classes as a matter of principle. “He was obnoxious, immature, a brat," a fellow student recalled. "What redeemed him was a keen, logical, beautiful mind."
Within 14 months of his arrival, Nash discovered the original idea that gained him a doctorate a few days before his 22nd birthday and would, many years later, win him a Nobel prize.
By the time Nash turned 30, he was a celebrity in the rarified world of mathematics. As a rising young academic, he had made astounding contributions not only in game theory but in several disparate branches of pure mathematics. Fortune magazine singled him out. A full professorship was around the corner. An MIT physics major who resembled Elizabeth Taylor yet displayed a certain steely resolve had fallen in love with him and was now his wife.
Then, like a curtain falling in the middle of a scene, the meteoric rise was over. One morning, Nash walked into the common room at MIT carrying a copy of the New York Times. He remarked, to no one in particular, that a story on the front page contained encrypted messages from inhabitants of another galaxy that only he could decipher. A graduate student was so intimidated by Nash’s intellect that he told no one when Nash took him aside, gave him an "intergalactic" driver’s license, and offered him a seat in his world government.
A mathematician from Harvard who visited Nash in the psychiatric hospital where he had been committed asked, “How could you, a mathematician committed to rationality, how could you believe that aliens from outer space were recruiting you to save the world?” Nash replied, “These ideas came to me the same way my mathematical ideas did, so I took them seriously."
The inability to distinguish between delusion and reality, between voices and one's own thoughts, is the tragedy of schizophrenia. We now know that schizophrenia is as "real" a disease as diabetes or cancer. But when Nash got sick, the science was primitive and so were the treatments.
By the 1980s the ideas Nash had in his twenties about conflict and cooperation were becoming influential in economics, political science and biology. But Nash, the man, was all but forgotten. Students around Princeton knew him only as the Phantom of Fine Hall, a mute, ghost-like figure who scribbled numerological messages on the blackboards of Princeton’s math building. Outside of a small circle of mathematicians and the loving wife who sheltered him, most people benefitting from his work simply assumed that its author was dead.
Then, after three decades, something extraordinary happened. Nash gradually recovered from the illness that most people regarded as a life sentence. “It was beautiful," a Princeton physicist recalled. "Slowly, he just somehow woke up.”
In October, 1994, Nash’s remarkable story was about to become public with the announcement of the Nobel Prize in Economics. What few learned until several years later was that Nash was nearly denied the ne plus ultra of intellectual honors. Literally one hour before the award was to be announced it was nearly voted down in an unprecedented refusal by many members of the Swedish Academy of Sciences to affirm the prize committee's choice. They feared that honoring a "madman" would sully the Nobel brand and spoil the prize ceremony. Ultimately, those who held that a mental illness should be no more of a bar than, say, heart disease, prevailed, but only narrowly.
"We resurrected him in a way," the chairman of the prize committee said proudly. Recognition proved a balm for many ills. The prize paved the way for getting back a life... not all that was lost, of course, but little things like a driver's license and dinner invitations and big ones like a research post, reconciling with his older son and obtaining treatment for his younger son.
The old, dry humor came back too. At the ceremony where he and Alicia repeated their marriage vows, Nash was asked to kiss her again for a photo. "A second take?" he shot back. "Just like the movies!"
And it was.
Sylvia Nasar
author, A Beautiful Mind: Genius, Madness, Reawakening
At one point in the film A Beautiful Mind, when it looked as if things were all over for John Nash, his wife Alicia takes his hand and places it over her heart and says, “I have to believe that something extraordinary is possible.”
Again and again in a life that encompassed genius, madness and reawakening, the extraordinary was possible.
At Princeton in the late 1940s, the 20-year old West Virginian was conspicuous for his movie star looks and Olympian manner. He was six feet, one inch tall, heavily muscled. He wore his fingernails unusually long. His conversation had a stilted, ornamental quality. He avoided classes as a matter of principle. “He was obnoxious, immature, a brat," a fellow student recalled. "What redeemed him was a keen, logical, beautiful mind."
Within 14 months of his arrival, Nash discovered the original idea that gained him a doctorate a few days before his 22nd birthday and would, many years later, win him a Nobel prize.
By the time Nash turned 30, he was a celebrity in the rarified world of mathematics. As a rising young academic, he had made astounding contributions not only in game theory but in several disparate branches of pure mathematics. Fortune magazine singled him out. A full professorship was around the corner. An MIT physics major who resembled Elizabeth Taylor yet displayed a certain steely resolve had fallen in love with him and was now his wife.
Then, like a curtain falling in the middle of a scene, the meteoric rise was over. One morning, Nash walked into the common room at MIT carrying a copy of the New York Times. He remarked, to no one in particular, that a story on the front page contained encrypted messages from inhabitants of another galaxy that only he could decipher. A graduate student was so intimidated by Nash’s intellect that he told no one when Nash took him aside, gave him an "intergalactic" driver’s license, and offered him a seat in his world government.
A mathematician from Harvard who visited Nash in the psychiatric hospital where he had been committed asked, “How could you, a mathematician committed to rationality, how could you believe that aliens from outer space were recruiting you to save the world?” Nash replied, “These ideas came to me the same way my mathematical ideas did, so I took them seriously."
The inability to distinguish between delusion and reality, between voices and one's own thoughts, is the tragedy of schizophrenia. We now know that schizophrenia is as "real" a disease as diabetes or cancer. But when Nash got sick, the science was primitive and so were the treatments.
By the 1980s the ideas Nash had in his twenties about conflict and cooperation were becoming influential in economics, political science and biology. But Nash, the man, was all but forgotten. Students around Princeton knew him only as the Phantom of Fine Hall, a mute, ghost-like figure who scribbled numerological messages on the blackboards of Princeton’s math building. Outside of a small circle of mathematicians and the loving wife who sheltered him, most people benefitting from his work simply assumed that its author was dead.
Then, after three decades, something extraordinary happened. Nash gradually recovered from the illness that most people regarded as a life sentence. “It was beautiful," a Princeton physicist recalled. "Slowly, he just somehow woke up.”
In October, 1994, Nash’s remarkable story was about to become public with the announcement of the Nobel Prize in Economics. What few learned until several years later was that Nash was nearly denied the ne plus ultra of intellectual honors. Literally one hour before the award was to be announced it was nearly voted down in an unprecedented refusal by many members of the Swedish Academy of Sciences to affirm the prize committee's choice. They feared that honoring a "madman" would sully the Nobel brand and spoil the prize ceremony. Ultimately, those who held that a mental illness should be no more of a bar than, say, heart disease, prevailed, but only narrowly.
"We resurrected him in a way," the chairman of the prize committee said proudly. Recognition proved a balm for many ills. The prize paved the way for getting back a life... not all that was lost, of course, but little things like a driver's license and dinner invitations and big ones like a research post, reconciling with his older son and obtaining treatment for his younger son.
The old, dry humor came back too. At the ceremony where he and Alicia repeated their marriage vows, Nash was asked to kiss her again for a photo. "A second take?" he shot back. "Just like the movies!"
And it was.
Sylvia Nasar
author, A Beautiful Mind: Genius, Madness, Reawakening
Brought to you by
Gillian Hawley